A key aspect of Wiles’ proof of Fermat’s Last Theorem is the modularity theorem. The proof crucially relies on the deep connection between Galois representations and LL-functions of elliptic curves. In recent years, mathematicians have continued to work on the modularity theorem, seeking various generalizations and proposing many related conjectures. In this talk, I will present an algorithm to compute the local Galois representation of an arbitrary curve via its semistable reduction.